The three dimensional shape information of teeth from cone beam computed tomography images provides important assistance for dentist performing implant treatment, orthodontic surgery. This paper describes the tooth root of both anterior and posterior teeth from CBCT images of head. The segmentation is done using level set method with five energy functions. The edge energy used to move the curve towards border of the object. The shape prior energy provides the shape of the contour. The dentine wall energy provides interaction between the neighboring teeth and prevent shrinkage and leakage problem. The test result for both segmentation and 3D reconstruction shows that the method can visualize both anterior and posterior teeth with high accuracy and efficiency.

1. Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
DOI:10.5121/acii.2016.3301 1
STUDY ANALYSIS ON TEETH SEGMENTATION
USING LEVEL SET METHOD
K.NITHYAKALYANIGOMATHI1
and R.JENSI2
1
Department of Computer Science and Engineering, Dr.Sivanthi Aditanar College of
Engineering, Tiruchendur.
2
Department of Computer Science and Engineering, Dr.Sivanthi Aditanar College of
Engineering, Tiruchendur.
ABSTRACT
The three dimensional shape information of teeth from cone beam computed tomography images provides
important assistance for dentist performing implant treatment, orthodontic surgery. This paper describes
the tooth root of both anterior and posterior teeth from CBCT images of head. The segmentation is done
using level set method with five energy functions. The edge energy used to move the curve towards border
of the object. The shape prior energy provides the shape of the contour. The dentine wall energy provides
interaction between the neighboring teeth and prevent shrinkage and leakage problem. The test result for
both segmentation and 3D reconstruction shows that the method can visualize both anterior and posterior
teeth with high accuracy and efficiency.
KEYWORD
Level set, cone beam computed tomography, tooth segmentation
1. Introduction
1.1 Related work
Dental x-rays provide two dimensional shapes of the teeth. The two dimensional view of tooth
root do not provide an accurate shape. In dental treatment, the accurate shape of teeth and root
plays an important role. Hence, three dimensional views of teeth used to represent an accurate
spatial orientation of tooth roots which is used for dental treatment such as orthodontic treatment.
The crown and root information must be clear which avoids treatment simulation. Thus we use
tomography scan image. In orthodontic treatment, dentists will gradually move teeth from
original position to target position. The Multi Slice Computed Tomography (MSCT) is used to
obtain 3D images with high amount of ionizing radiation which may leads to cancer. Nowadays,
the dentists using Cone Beam Computed Tomography (CBCT) image for treatment due to lower
radiation.
There are various segmentation algorithms to extract root from the teeth. In adaptive threshold
method [5] under segmentation or over segmentation problem occur due to non homogeneous
intensity distribution inside teeth. Edge based segmentation methods [11] fails to segment the
tooth boundary. The region based segmentation [2] fails to separate the object when region inside
the region of interest has similar intensity value. The intensity distributions and edge information
are combined in hybrid segmentation method [8] so tooth boundary can be easily segmented. It

2. Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
2
fails to avoid shrinking and leakage problem. The extraction of root of the teeth is designed by
distance regularized level set evolution (DRLSE) [7]. This method is applied for orthodontic
treatment but it fails to segment the small portion of the root [1].
The level set method [3] with five energy function is applied to segment the anterior teeth. In our
proposed system we applied these energy functions for both anterior teeth and posterior teeth.
2. ENERGY BASED APPROACH
The adjacent teeth segmentation problem can be avoided by external edge energy which gives the
desired edge of the teeth. The tooth root is segment into tooth pulp and tooth dentine. The energy
based approach computationally derives to segment the object. Figure 1 show the methodology to
segment the teeth.
Figure 1. System model for segmenting the teeth
2.1 GAUSSIAN FILTER
Images are often corrupted by variation in intensity and illumination value which can not be
directly applied so we apply some filter to image. Gaussian smoothing operator is used to blur
images and remove detail and noise. Gaussian filter is a non-uniform low pass filter works by
using 2D distribution as a point spread function. Gaussian filter is more effective at smoothing
image. It has its basis in human visual perception system. Gaussian kernel coefficient are sampled
from 2D Gaussian function,
, =
²
^
+ ²
2²
(2.1)
In one dimension, Gaussian function is
, =
√ ²
² 2²
⁄ (2.2)
Where σ is standard deviation of distribution.
2.2 LEVEL SET SEGMENTATION
Level set segmentation is a generic numerical method for evolving fronts in an implicit form. The
central idea is to represent the evolving contour using a signed distance function. The distance
function is negative inside the curve and positive outside. By choosing a suitable speed function
F, we may segment an object in an image. The standard level set segmentation speed function is:
F=1–єκ+β(. |I|) (2.3)
Input Image Gaussian
Filter
Segmentation
3D view
of
segmented
teeth

3. Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
3
Where 1 causes contour to inflate inside the object.
-єκ (viscosity) term reduces the curvature of the contour.
edge attraction term pulls the contour to the edges.
It can be used to efficiently address the problem of curves propagation in an implicit manner. It
handles topological changes of the evolving interface. The re-initialization method of level set
function fails to assign the original place of contour [6]. According to Dong Xu Ji and Sim Heng
Ong [3] the level set function φ can develop shocks, very sharp and flat shape during the
evolution, which makes inaccurate computation. To avoid these problems, a common numerical
scheme is to assign signed distance function before the evolution and then reshape the function φ
periodically during the evolution. Thus the level set is applied with five energy term as shown in
Eq. (2.4)
JR(C) = λ1J1(C)+λ2J2(C)+λ3J3(C)+λ4J4(C)+λ5J5(C) (2.4)
Where,
JR(C) – total energy term to segment the tooth root.
J1(C) – penalizing energy term.
J2(C) – the region energy term.
J3(C) – edge energy term.
J4(C) – shape prior energy term.
J5(C) – the dentine wall thickness energy term.
λi – weight for the ith
energy term.
According to the energy function the above equation can be rewritten as
J(φ)=λ1J1(φ)+λ2J2(φ)+λ3J3(φ)+λ4J4(φ)+λ5J5(φ) (2.5)
2.2.1. PENALIZING ENERGY:
J1(φ)= ½|| − 1 (2.6)
Where is the gradient operator. During evolution, the deviation of φ is penalized from signed
distance function. This avoids time consuming re-initialization step of level set method.
2.2.2 REGION ENERGY:
The segmentation is to segment the region into two regions, the object region Ω1 and the
background region Ω2. This can be done using the region based model using the intensity
distributions difference. The contour is derived by maximizing the likelihood function:
J0(C)=p(u|C,M1,M2) (2.7)
Where p(u|C,M1,M2) is the joint probability density function for intensities u given the contour C
and the two models. The intensity distribution within each region and the contour C is the zero
level of the SDF φ is shown in Eq. (2.8).
J2(φ)=ʃ-ln(p1(u(x,y)|Ω1)H(-φ)dxdy+ʃ-ln(p2(u(x,y)|Ω2)(1-H(-φ))dxdy (2.8)

4. Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
4
2.2.3 EDGE ENERGY:
The edge based term pulls the contour C to the edges of the image. This is evaluated by
minimizing the following functional:
J3(φ)=ʃCgds (2.9)
Where ds represent the Euclidean arc length of C, φ is the SDF of C.
J3(φ)=ʃΩgδ(φ)|φ|dxdy (2.10)
Where g is the positive and decreasing function serving as an edge detector and δ is the smoothed
dirac function given by,
δє(z)=1/2є[1+cos(Πz/є)],if|z|=є (2.11)
2.2.4 SHAPE PRIOR ENERGY:
The shape prior term is used to evolve the contour C to the final segmentation contour C0 in Eq.
(2.12). The point model is used to derive the boundaries of the shape [10]. The equal weights are
given to all pixels in shape prior [4].
J4(C) = ʃC φ0 ²(x,y) ds (2.12)
Where φ0 is the SDF of the segmented tooth region of previous slice, φ is the SDF of C.
J4(φ) = ʃΩφ0 ²(x,y) δ(φ) |φ| ds (2.13)
2.2.5 DENTINE WALL THICKNESS ENERGY:
The dentine is the area between the enamel and the tooth. The tooth pulp is used to refine the
contour by penalizing the tooth dentine thickness where the dentine wall is thin. Define
D((x,y),Cp) as the distance between a point and the curve Cp, and D(C,Cp) as the collection of all
such distance of points on C. Davg denotes the average value of Dthin(x,y).
φt(x,y) = φp(x,y) – Davg (2.14)
Where φp(x,y) is the SDF of the contour of the tooth pulp Cp, φt(x,y) is the SDF of the shape
which is an enlarged version of the tooth pulp.
J5(φ) = ʃΩ φt(H(φt) – H(φ)) dx dy (2.15)
2.2.6 OVERALL ENERGY FUNCTIONAL:
Summing up five energy function is shown in Eq. (2.16).
J(φ)= λ1 ʃΩ½ (|φ|-1)² dx dy +
λ2 (ʃΩ - ln (p1) H(-φ) dx dy + ʃΩ - ln (p2) (1-H(- φ)) dx dy)
+ λ3 ʃΩ gδ(φ) |φ| dx dy
+ λ4 ʃΩ φ0 ²δ(φ)|φ| dx dy
+ λ5 ʃΩ φt (H(φt) – H(φ)) dx dy. (2.16)

5. Advanced Computational Intelligence: An International Journal
This energy function leads to 1000 iteration to segment the object in the image. In evolution of
this iteration the contour will shrink to reach the boundary of the teeth.
based on the value of shape prior term.
2.3 3D RECONSTRUCTION
3D reconstruction is the process of capturing the shape and appearance of tooth from various
slices. The dentistry requires accurate 3D representation of the teeth and jaw for diagnostic and
treatment purposes. It is based on the shading of the image,
image. The accuracy of teeth is increased using shape from shading
The accurate segmentation of the root of a buried tooth such as buried upper canine and the
neighboring teeth structures provides o
trajectories and pathways for moving the buried canine into the dental arch. The segmented
individual teeth of every slice of CBCT scan image is combined together to form a 3D complete
view of teeth.
3. EXPERIMENTS AND RESULTS
We have applied this procedure for 12 patients CBCT scan image
patient’s head obtaining up to nearly 600 distinct slice images.
to remove noise as shown in Figure 2
deviation 1.5 to suppress noise.
Figure 2: Original CBCT scan image and smoothing image
The level set method is applied to each slicing image and the result is saved in database.
contour is drawn using volume along with surface of image [12
the relative scaling units. First we segment the crown and then root.
Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
This energy function leads to 1000 iteration to segment the object in the image. In evolution of
iteration the contour will shrink to reach the boundary of the teeth. The iteration value is
based on the value of shape prior term.
3D reconstruction is the process of capturing the shape and appearance of tooth from various
The dentistry requires accurate 3D representation of the teeth and jaw for diagnostic and
treatment purposes. It is based on the shading of the image, 3D points and smoothness of the
cy of teeth is increased using shape from shading with 2D PCA shape priors.
The accurate segmentation of the root of a buried tooth such as buried upper canine and the
neighboring teeth structures provides orthodontics a clear 3D anatomic map for simulating
trajectories and pathways for moving the buried canine into the dental arch. The segmented
individual teeth of every slice of CBCT scan image is combined together to form a 3D complete
ESULTS
We have applied this procedure for 12 patients CBCT scan image. CBCT scanner rotates around
patient’s head obtaining up to nearly 600 distinct slice images. The Gaussian filter is applied first
as shown in Figure 2. We choose Gaussian filter of size 15 x 15 and standard
Figure 2: Original CBCT scan image and smoothing image
The level set method is applied to each slicing image and the result is saved in database.
along with surface of image [12]. The data aspect ratio determines
First we segment the crown and then root.
, No.3, July 2016
5
This energy function leads to 1000 iteration to segment the object in the image. In evolution of
The iteration value is
3D reconstruction is the process of capturing the shape and appearance of tooth from various
The dentistry requires accurate 3D representation of the teeth and jaw for diagnostic and
3D points and smoothness of the
with 2D PCA shape priors.
The accurate segmentation of the root of a buried tooth such as buried upper canine and the
rthodontics a clear 3D anatomic map for simulating
trajectories and pathways for moving the buried canine into the dental arch. The segmented
individual teeth of every slice of CBCT scan image is combined together to form a 3D complete
. CBCT scanner rotates around
The Gaussian filter is applied first
We choose Gaussian filter of size 15 x 15 and standard
The level set method is applied to each slicing image and the result is saved in database. The
]. The data aspect ratio determines

6. Advanced Computational Intelligence: An International Journal
Figure 3. Red line displays
The coupled level set method is used to segment the crown and tooth dentine contour is used to
segment the root. The segmentation is applied from initial slice to root tip for individual teeth as
shown in Figure 3. This segmentation result is more accurate
is done using matlab. Collection of segmented results in three dimensional axial
display the teeth. We applied this segmentation technique for posterior teeth which have multiple
roots. The average time consume per teeth is 228 s.
4. CONCLUSION
This study presents a level set algorithm to detect the contour of the anterior and posterior teeth.
In this method the topology tooth changes when root splits. The averag
this method than the Dong Xu Ji method.
quality. The tooth dentine wall avoids leakage problem.
shrinking problem. The adjacent teeth are segmented
varying for each individual tooth. Thus this can be improved by the gray value distribution
around the root. Using this method we try to segment the whole tooth set of the patient by which
dentist can improve treatment process.
segmentation results for both anterior and posterior teeth of the patients. In future autom
segmentation technique is created to detect the tooth, thus the dentistry can easily diagnosis the
treatment in timely manner.
Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
line displays the segmentation results for single slice.
The coupled level set method is used to segment the crown and tooth dentine contour is used to
segment the root. The segmentation is applied from initial slice to root tip for individual teeth as
shown in Figure 3. This segmentation result is more accurate and efficient. The 3D reconstruction
is done using matlab. Collection of segmented results in three dimensional axial views
We applied this segmentation technique for posterior teeth which have multiple
consume per teeth is 228 s.
Figure 4. 3D view of premolar teeth
This study presents a level set algorithm to detect the contour of the anterior and posterior teeth.
In this method the topology tooth changes when root splits. The average time consume is less in
this method than the Dong Xu Ji method. The accuracy of segmentation depends on image
quality. The tooth dentine wall avoids leakage problem. The shape and intensity value avoids
shrinking problem. The adjacent teeth are segmented carefully. The root profile value may be
varying for each individual tooth. Thus this can be improved by the gray value distribution
Using this method we try to segment the whole tooth set of the patient by which
dentist can improve treatment process. This method provides more accurate and robust
segmentation results for both anterior and posterior teeth of the patients. In future autom
segmentation technique is created to detect the tooth, thus the dentistry can easily diagnosis the
, No.3, July 2016
6
The coupled level set method is used to segment the crown and tooth dentine contour is used to
segment the root. The segmentation is applied from initial slice to root tip for individual teeth as
and efficient. The 3D reconstruction
views used to
We applied this segmentation technique for posterior teeth which have multiple
This study presents a level set algorithm to detect the contour of the anterior and posterior teeth.
e time consume is less in
The accuracy of segmentation depends on image
The shape and intensity value avoids
The root profile value may be
varying for each individual tooth. Thus this can be improved by the gray value distribution
Using this method we try to segment the whole tooth set of the patient by which
This method provides more accurate and robust
segmentation results for both anterior and posterior teeth of the patients. In future automatic
segmentation technique is created to detect the tooth, thus the dentistry can easily diagnosis the

7. Advanced Computational Intelligence: An International Journal (ACII), Vol.3, No.3, July 2016
7
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